Evaluating and dividing polynomials (4 problems) do all and show work please.

The sum of the 3rd triangular, 4th square, 5th pentagonal, 6th hexagonal, 7th heptagonal, and 8th octagonal numbers is 384.

What is triangle ?

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted triangle ABC.

The nth triangular number is given by the formula: n(n+1)/2

The nth square number is given by the formula: n^2

The nth pentagonal number is given by the formula: n(3n-1)/2

The nth hexagonal number is given by the formula: n(2n-1)

The nth heptagonal number is given by the formula: n(5n-3)/2

The nth octagonal number is given by the formula: n(3n-2)

So, the sum of the 3rd triangular number, 4th square number, 5th pentagonal number, 6th hexagonal number, 7th heptagonal number and 8th octagonal number can be calculated as follows:

Triangular number: 3 * (3 + 1) / 2 = 6

Square number: 4^2 = 16

Pentagonal number: 5 * (3 * 5 - 1) / 2 = 35

Hexagonal number: 6 * (2 * 6 - 1) = 91

Heptagonal number: 7 * (5 * 7 - 3) / 2 = 98

Octagonal number: 8 * (3 * 8 - 2) = 128

The sum of these numbers is: 6 + 16 + 35 + 91 + 98 + 128 = 384.

So, the sum of the 3rd triangular, 4th square, 5th pentagonal, 6th hexagonal, 7th heptagonal, and 8th octagonal numbers is 384.

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The sum of the 3rd triangular, 4th square, 5th pentagonal, 6th hexagonal, 7th heptagonal, and 8th octagonal numbers is 384.

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted triangle ABC.

The nth triangular number is given by the formula: n(n+1)/2

The nth square number is given by the formula: n^2

The nth pentagonal number is given by the formula: n(3n-1)/2

The nth hexagonal number is given by the formula: n(2n-1)

The nth heptagonal number is given by the formula: n(5n-3)/2

The nth octagonal number is given by the formula: n(3n-2)

So, the sum of the 3rd triangular number, 4th square number, 5th pentagonal number, 6th hexagonal number, 7th heptagonal number and 8th octagonal number can be calculated as follows:

Triangular number: 3 * (3 + 1) / 2 = 6

Square number: 4² = 16

Pentagonal number: 5 * (3 * 5 - 1) / 2 = 35

Hexagonal number: 6 * (2 * 6 - 1) = 91

Heptagonal number: 7 * (5 * 7 - 3) / 2 = 98

Octagonal number: 8 * (3 * 8 - 2) = 128

The sum of these numbers is: 6 + 16 + 35 + 91 + 98 + 128 = 384.

So, the sum of the 3rd triangular, 4th square, 5th pentagonal, 6th hexagonal, 7th heptagonal, and 8th octagonal numbers is 384.

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The equivalent fraction to 4/6 with a denominator of 12 is:

4/6 = 8/12

If we have any fraction a/b, to find a equivalent fraction we just need to multiply both numerator and denominator by the same number (different than zero)

Here we want to find an equivalent fraction to 4/6, such that the new denominator is 12, then we can multiply both numerator and denominator by 2.

We will get:

4/6 = (2*4)/(2*6) = 8/12

So these two are equivalent fractions:

4/6 = 8/12.

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Answer: Let p: Triangle is equilateral. Let q: Triangle is isosceles. Then the symbolic form of the given statement is p ∨ q.

Step-by-step explanation:

The application of the identity tan(a+b) = (tan(a)+tan(b))/(1-tan(a)tan(b)).the result tan(2x) = 2*tan(x)/(1 - tan²(x)).

Statement | Reason

Tangent (2x) | Given= tangent (x + x) | 1= startfraction tangent (x) + tangent (x) over 1 minus tangent (x) tangent (x) endfraction | 2= startfraction 2 tangent (x) over 1 minus tangent squared (x) endfraction | 3.Reason 1 is the application of the identity tan(a+b) = (tan(a)+tan(b))/(1-tan(a)tan(b)). Reason 2 is the application of the identity tan(2x) = 2*tan(x)/(1 - tan²(x)). Reason 3 is the result of the two previous steps, which is the solution to tan(2x). By applying the identities, we have derived the result tan(2x) = 2*tan(x)/(1 - tan²(x)).

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Answer:

Reason 1 is - Addition

Reason 2 is - Tangent Sum Identity

Reason 3 is - Simplify

Step-by-step explanation:

edge

The output of the function can be calculated by plugging in 2 for x and evaluating the equation:[tex]f(2) = 2(2^3) + 5(2^2) - 7(2) + 4 = 16 + 20 - 14 + 4 = 26.[/tex]

The Common Core standards for Pre-Calculus focus on the study of functions and their applications, as well as the development of a deeper understanding of the algebraic and geometric principles in the mathematical field. One of the core concepts covered in Pre-Calculus is the concept of polynomial functions. A polynomial function is an expression made up of terms that involve only constants, variables, and exponents. It is represented by the equation [tex]f(x) = ax^n + bx^n-1 + cx^n-2 + … + z[/tex], where a, b, c, …, z are constants and n is a non-negative integer. To find the value of a polynomial function at a given value of x, the equation can be evaluated by plugging in the x value and calculating the output. For example, if a polynomial function is represented by the equation f(x) = 2x^3 + 5x^2 - 7x + 4, and the x value is 2, then the output of the function can be calculated by plugging in 2 for x and evaluating the equation: [tex]f(2) = 2(2^3) + 5(2^2) - 7(2) + 4 = 16 + 20 - 14 + 4 = 26.[/tex]

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Complete question:

What is the output of the polynomial function f(x) = 2x^3 + 5x^2 - 7x + 4 when x = 2?

Answer:

the answer to it is y = -2x + 8

Step-by-step explanation:

Answer:

6x-3y=12 equals -3y=-6x+12 equals y=2x-4. In slope-intercept form; y=mx+c, m is slope and c is the y-value of the intercept; (0,y). So the slope is 2, and the y-intercept is -4 or (0,-4). answer.

Step-by-step explanation:

pls, tell me if wrong have a good day/night<3

If two line segments are parallel to each other and the first line segment has endpoints at (2, 3) and (1,9) while the second line segment has endpoints at (5, 4) and (3,Y), the value of y is:

16

Two lines are parallel if and only if they have the same slope. So, to find the value of y, we need to find the slope of the first line segment and use it to find the equation of the second line segment.

The slope of the first line segment can be found using the formula:

Since the two lines are parallel, they have the same slope, so we can use the slope to find the equation of the second line segment.

Expanding the equation and solving for y, we get:

Now that we have the equation of the second line segment, we can use the x-coordinate of one of its endpoints (3) to find the corresponding y-coordinate.

So, the value of y is 16.

Complete Question:

"Two line segments are parallel to each other. The first line segment has endpoints at (2, 3) and (1,9). The second line segment has endpoints at (5, 4) and (3,Y).

What is the value of y?

A. 34

В. 16

C. 10

D. 6"

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The area of the pool is 113.04 ft².

The diagram shows a circle inside a square. The circular surface is the pool and it is surrounded by the square deck. The diameter of the pool can be chosen from 12 to 24 feet.

The blue shaded region is the area of the pool. Therefore, let's find the area of the pool as follows:

area of the pool(area of a circle) = πr²

where

Therefore,

r = diameter / 2 = 12 / 2 = 6 feet

Hence,

area of the pool(area of a circle) = 3.14 × 6²

area of the pool(area of a circle) = 3.14 × 36

area of the pool(area of a circle) = 113.04 ft²

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The domain of the function f(x) = 10x + 8 will be all x values such that 0 ≤ x < 248.

The domain of a function is the set of all possible input values for which the function is defined. For the function f(x) = 10x + 8, the domain will be all real numbers greater than or equal to 0. This can be seen by examining the equation: if x = 0, then f(x) = 8. Therefore, the domain of the function will be all x values such that x ≥ 0. To calculate the upper bound for the domain, we can solve for x by subtracting 8 from both sides of the equation, resulting in 10x = -8. Dividing both sides by 10 gives us x = -0.8. Therefore, the domain of the function f(x) = 10x + 8 will be all x values such that 0 ≤ x < 248.

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The  equation that can be used to solve for x, the total amount of paint in the mixture of the two colors is: 0.15(40) + 0.6(x - 40) = 0.25(x).

We need to solve for x,

6+0.6x - 24=0.25x

After rearranging the equation we get,

0.35x=18

Divide both side by 0.35x

x=18/0.35

x = 51.43

The  equation that can be used to solve for x, the total amount of paint in the mixture of the two colors is: 0.15(40) + 0.6(x - 40) = 0.25(x).

Inconclusion the equation that can be used to solve for x, the total amount of paint in the mixture of the two colors is: 0.15(40) + 0.6(x - 40) = 0.25(x).

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. The meanings of the word equation and its cognates in other languages can vary slightly. For instance, an equation is described as having one or more variables in French.

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Complete question: Fifteen percent of the pigment in paint color A is black. Sixty percent of the pigment in paint color B is black. An unknown amount of paint color B is mixed with 40 ml of paint color A, resulting in a paint that contains 25% black pigment.

Which equation can be used to solve for x, the total amount of paint in the mixture of the two colors?

The correct option: a) O quantitative data;  defines the cost of the theater ticket.

Data that expresses a definite quantity, amount, or range is known as quantitative data.

Thus, the cost of any theater ticket defines an example of quantitative data.

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After solving the set we get three unknowns and two equation. So the set S does not spans r^2.

A geometric description of the subspace:

s = {(−1, 4), (4, −1), (3, 3)}

Let the element of R^2 be (x, y).

(x, y) = [tex]c_{1}[/tex](-1, 4) + [tex]c_{2}[/tex](4, −1) + [tex]c_{3}[/tex](3, 3)

(x, y) = (-1[tex]c_{1}[/tex] + 4[tex]c_{2}[/tex] + 3[tex]c_{3}[/tex], 4[tex]c_{1}[/tex] - 1[tex]c_{2}[/tex] + 3[tex]c_{3}[/tex],)

Now the value of

x = -1[tex]c_{1}[/tex] + 4[tex]c_{2}[/tex] + 3[tex]c_{3}[/tex]

y = 4[tex]c_{1}[/tex] - 1[tex]c_{2}[/tex] + 3[tex]c_{3}[/tex]

x - y = -1[tex]c_{1}[/tex] + 4[tex]c_{2}[/tex] + 3[tex]c_{3}[/tex] - (4[tex]c_{1}[/tex] - 1[tex]c_{2}[/tex] + 3[tex]c_{3}[/tex])

x - y = -1[tex]c_{1}[/tex] + 4[tex]c_{2}[/tex] + 3[tex]c_{3}[/tex] - 4[tex]c_{1}[/tex] + 1[tex]c_{2}[/tex] - 3[tex]c_{3}[/tex]

As we can see that there have three unknown and two equations. So we can not solve them.  So the set S does not span R^2.

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The graph of the exponential function:

f(x) = 2*(3)^x

Is the first one.

We want to find the graph of the exponential function:

f(x) = 2*(3)^x

To identify it, you can evaluate the function in some different values of x.

if x = 0

f(0) = 2*(3)^0 = 2

if x = 1

f(1) = 2*3^1 = 6

if x = 2

f(2) = 2*(3)^2 = 18

So we have the 3 points:

(0, 2), (1, 6), (2, 18)

The only graph that passes through these points is the first one, so that is the correct option.

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There are eight multiples: 8, 16, 24, 32, 40, 48, 56, 64, 72, and so on.

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Answer: Diploid cells divide to form four haploid daughter cells during mitosis.

Step-by-step explanation:

The answer is: Sister chromatids separate to form haploid daughter cells during meiosis.

One of a chromosome's two identical halves that has undergone replication in order to facilitate cell division is referred to as a chromatid. A chromosomal region known as the centromere is where the two "sister" chromatids are fused.

One of the two identical copies of a duplicated chromosome is called a chromatid. At the centromere, a portion of the chromosome, the twin copies of the DNA join together during cell division. Sister chromatids are those that are joined. A chromosome is a protein and DNA-based structure that resembles a thread. It contains an organism's whole genetic makeup. Parents pass this on to their children. One of a chromosome's halves is called a chromatid. There is just one chromatid per chromosome.

The chromatids in each thread-like structure in the chromosome are the result of the chromosome's DNA replicating itself. Haploid cells are produced as a result of the segregation of the chromatids during meiosis II.

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The complete question is as follows:

The area of mathematics known as probability explores potential outcomes of events, along with the likelihoods and distributions of those occurrences.

What is meant by probability?

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability. Calculating a result or an event's likelihood is known as simple probability. To calculate the likelihood of having to pay out a claim, insurance firms employ probability statistics. A simple probability is computed by dividing a particular result by all potential results.

There are now 36 distinct ways the dice can land when two of them are rolled. This amount is calculated by multiplying the first die's possible outcomes (six) by the second die's possible outcomes (six). 6 x 6 = 36.

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The largest interval I over which the general solution is defined is (-∞, ∞).

A differential equation is a mathematical equation that relates an unknown function to its derivatives. It expresses the relationship between an dependent variable (the unknown function) and one or more independent variables. Differential equations are used to model physical, biological, and economical systems, among others.

A differential equation can be thought of as an equation that describes how a function changes over time. For example, the velocity of an object is the derivative of its position with respect to time. If the position of the object is modeled by a function, then its velocity can be described by a differential equation.

ODEs deal with functions of a single variable and their derivatives, while PDEs deal with functions of multiple variables and their partial derivatives.

The given differential equation is a first-order linear ordinary differential equation with constant coefficients:

dy/dx + y = e⁷ˣ

This equation can be solved using the method of integrating factors. The integrating factor is given by e^∫1 dx = e^x. Multiplying both sides of the equation by the integrating factor, we get:

eˣ(dy/dx) + eˣ y = e⁸ˣ

Integrating both sides, we get:

eˣ y = e⁸ˣ - eˣ + C, where C is an arbitrary constant of integration.

Dividing both sides by eˣ, we get the general solution:

y = e⁷ˣ + Ce⁻ˣ

The largest interval I over which the general solution is defined is (-∞, ∞).

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Value of is in the plane spanned will be -2[1,2,-1] - 3[-2,-1,1] = [4,-1,-1].

If y is on the plane covered by v1 and v2, v1 and v2 can be combined linearly to form y.

Y is equal to av1 plus bv2, where a and b are constants.

[4,-1,h] = a[1,2,-1] + b[-2,-1,1]

According to the laws of vector addition and multiplication, [4,-1,h] = [a - 2b,2a - b, -a + b]. A vector is equal if each of its components is equal.

4 = a - 2b

-1 = 2a - b

h = -a + b

From the first two equations, we can solve for a and b to obtain h:

a = -2

b = -3

h = -1

As we can see, -2[1,2,-1] - 3[-2,-1,1] = [4,-1,-1].

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Full Question:

For what value of h is y in the plane spanned by v1 and v2?

1 fluid Pint (U.S.) = 16 fluid Ounces (US)

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The real values of x are -10 and 10

From the question, we have the following parameters that can be used in our computation:

(x^2 - 82)^2 = 324

Take the square roots of both sides

So, we have

x^2 - 82 = 18

Add 82 to both sides of the equation

So, we have the following representation

x^2 = 100

Take the square root of both sides

x = -10 and x =10

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By definition of midpoint, the coordinates of B is (- 5, 4).

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

We have to given that;

The midpoint of AB is M (-2, 1).

And, The coordinates of A are (1,−2).

Now, Let the coordinate of B = (x, y)

Then, By definition of midpoint we get;

⇒ (1 + x) / 2 = - 2

⇒ 1 + x = - 4

⇒ x = - 4 - 1

⇒ x = - 5

⇒ (- 2 + y) / 2 = 1

⇒ - 2 + y = 2

⇒ y = 2 + 2

⇒ y = 4

Thus, The coordinate of B = (- 5, 4)

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The probability that each of the balls will be of a different color is approximately 0.084.

To calculate the probability that each of the balls will be of a different color, we need to consider all possible combinations of 3 balls from the urn. There are a total of 19 balls in the urn, so there are 19 choose 3, or 19!/(3! * (19-3)!) = 191817/3! = 969 possible combinations.

Of these 969 combinations, there are

5 choose 1 * 6 choose 1 * 8 choose 1 = 5 * 6 * 8 = 240 combinations where each of the 3 balls is of a different color. So, the probability that each of the balls will be of a different color is 240/969 = 0.084, or approximately 0.084.

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Answer:

a line

Step-by-step explanation:

2 points make a line

Answer A Line

Step-by-step explanation:

a) The length of the base is 10 units and the height is 7 units. The area is 35 square units.

B) The length of the base is 10 units and the height is 6 units. The area is 30 square units.

C) The length of the base is 10 units and the height is 3 units. The area is 15 square units.

D) The length of the base is 4 units and the height is 11 units. The area is 22 square units.

What is a triangle?

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

The base and height are highlighted in each triangle.

A)

The length of the base is 10 units.

The length of height is 7 units.

The area of the triangle is 1/2 × 10 × 7 = 35 square units.

B)

The length of the base is 10 units.

The length of height is 6 units.

The area of the triangle is 1/2 × 10 × 6 = 30 square units.

C)

The length of the base is 10 units.

The length of height is 3 units.

The area of the triangle is 1/2 × 10 × 3 = 15 square units.

D)

The length of the base is 11 units.

The length of height is 4 units.

The area of the triangle is 1/2 × 11 × 4 = 22 square units.

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Answer:

Step-by-step explanation:

The slope of a line can be found using the formula:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are two points on the line. Plugging in the given points, we get:

slope = (8 - 6) / (-5 - (-10)) = 2 / 5 = 0.4

So the slope of the line through the points (-10, 6) and (-5, 8) is 0.4

You need to work 84 hours per month at your second job to meet your monthly savings goal.

Fixed expenses = 2,034.24 x 30% = $610.72

Discretionary income = 2,034.24 - 610.72 = $1,423.52

Savings goal per month = $1,423.52 x 20% = $284.70

Net pay per hour = $9.50 - ($9.50 x 7.65%) - ($9.50 x 11.5%) - ($9.50 x 7.75%) = $7.33

Hours per month = $284.70 ÷ $7.33 = 84 hours.

To calculate, first find the number of your fixed expenses by multiplying your primary job income by 30%. This is $610.72. Then subtract your fixed expenses from your primary job income to find your discretionary income, which is $1,423.52. Multiply that by 20% to find the amount you want to save each month, which is $284.70.

Finally, divide that amount by your net pay per hour after taxes from your second job, which is $7.33, to find the number of hours you need to work, which is 84 hours.

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The curve for the relationship between balloon rides and price when the temperature is constant at 50 degrees is illustrated below.

The term constant in math is defined as  a value or number that never changes in expression it's constantly the same.

When the temperature is constant, it means that one of the variables that can affect the demand for balloon rides is eliminated. This allows us to focus on the relationship between balloon rides and price. The relationship between these two variables can be represented by a curve. The curve can show us how the price of a balloon ride changes as the number of rides changes.

Then table for the relationship between balloon rides and price when the temperature is constant at 50 degrees is attached below.

when the temperature is constant, the relationship between balloon rides and price can be shown by a curve. The shape of the curve will depend on the relationship between the two variables, which can be upward-sloping, downward-sloping, or remain constant. The constant temperature allows us to focus on the relationship between balloon rides and price without the interference of other factors that can affect the demand for rides.

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Answer:

Step-by-step explanation:

y=0,16/5